Mine blasting operations require knowledge of shock wave propagation, fracture mechanics and
the internal stress field of the rock mass. In this photograph of a Wyoming coal mine, explosives are
used to break up rock layers in order to loosen the coal seam.
(Photograph courtesy of Chuck Meyers, Office of Surface
Mining, U.S. Department of the Interior.)

COLORADO SCHOOL OF MINES CHOSE ALGOR SOFTWARE FOR EXPLOSIVES RESEARCH

Research in Shock Wave Propagation and Rock Fracture to Aid in Development of Explosives-Resistant
Materials to Help Fight Terrorism

Research performed at the Colorado School of Mines (CSM) in Golden, Colorado could
help in the war against terrorism. By studying how shock waves from the
detonation of a plastic explosive propagate through rock, researchers are gaining a better
understanding of fracture phenomena. Such knowledge can be applied to the
operation of mines and construction of protective walls that will absorb the shock waves of a
bomb.

According to Dr. Vilem Petr, Research Assistant Professor of CSM's Mining
Engineering Department, "We have established, under the leadership of department
head Dr. Tibor G. Rozgonyi, a close relationship with globally-recognized
explosives engineering organizations including Orica USA, Inc., Applied Research Associates, Inc.
and the International Society of Explosives Engineering. Additionally, we are working with the
Department of Defense, Department of Transportation and Defense Threat Reduction Agency on
developing 'smart' construction materials, such as explosives-resistant concrete, to protect military
personnel and equipment."

Petr said, "We still do not understand fracture phenomena completely. It is of the utmost
importance to develop a theoretical model validated with experimental data that provides a better
understanding of how shock wave energy, due to dynamic loading, is transmitted and reflected through
non-homogeneous geomedia with complex physical properties and grain boundaries. A more complete
understanding could lead to refinement of blasting techniques, which would lower
mine operation costs."

During the past three years, CSM researchers have conducted experimental and numerical studies of
shock wave propagation in a geomedium (a rock mass). Their physical experiments included use of
strain gauges and photoelastic material to determine the stress field inside a geomedia specimen.
Data from the experimental studies were used in numerical analyses including discrete element method
software developed at CSM and Mechanical Event Simulation (MES) software from ALGOR, Inc. to examine
shock wave effects more precisely. "We chose the ALGOR software because of its capabilities
for modeling multiple bodies and materials," said Petr. "Also, it was easy to learn, user-friendly
and a good value."

Experimental Studies

The researchers hypothesized that shock wave velocities traveling within a non-homogeneous
geomedium are affected by the geometrical arrangement of particles and differences in material
properties. "The packing of the material and the grain boundary can play a very important role in
rock fragmentation," explained Petr. "The shock wave can lose a lot of energy as it passes across
joints and through materials of different densities."

A diagram and photograph of a photoelastic experimental model. The photo shows mounted
strain gauges and a cone with its inner surface covered by plastic explosive on top of the model.

In order to study how shock waves propagate through various materials, test specimens were
constructed using discs made of photoelastic material, which represented
grains within a geomedium. A casting resin cemented the discs together. "We created a macrostructure model
of a microstructure," said Petr. The relative densities of
the discs and the cementing material were varied in different specimens to test
the effect of material density on shock wave velocity. The packing arrangement
of the discs was also varied to test how different patterns of grains might slow
down shock waves.

At the CSM Mining Engineering Department's laboratory, a test apparatus was constructed in which a photoelastic
specimen was mounted with strain gauges. A cone with its inner surface covered by plastic explosive was acoustically
coupled to the top of the specimen. When the plastic explosive was detonated, the cone directed a
planar shock wave perpendicular to the top surface of the specimen.

A high-speed camera photographed the event at a rate of one-million frames per
second, recording the growth of dynamic fringe patterns in the photoelastic material.
Examination of the fringe patterns indicated how the shock wave passed through the
photoelastic material. Measurements of fringe patterns and impact velocity were used to
calculate the stress field within the geomedia specimen.

"Since the advent of computer simulation, photoelastic experimentation is not used as much
because it is time-consuming, expensive and provides inconsistent results," said Petr.
"Still, it is another good tool for studying stress wave propagation inside a
geomedium since having experimental data to compare to numerical analysis is a great benefit."

A diagram of the experimental test setup.

Dr. Vilem Petr of the Colorado School of Mines holding a fractured photoelastic
experimental specimen.

Numerical Studies

According to Petr, the primary advantage of the DEM software, which was developed by Dr. Graham
Mustoe of CSM's Division of Engineering, was that it modeled the geomedium as a system of several
hundred rigid particles joined together elastically. "Discrete particles were well suited for
simulating the grain lattice," said Petr.

"ALGOR finite element analysis software provided advantages for modeling the multiple materials
of the geomedium," said Petr. "The surface-to-surface contact and automatic meshing capabilities
made it easy to model the interaction between different materials of different densities in various
packing configurations."

In the finite element model, initiation of the shock wave was simulated by impacting the top
surface of the specimen with a block moving at the same velocity as was measured in the physical
experiment. "The challenge was to make an FEA model of an explosion, which is a chemical reaction,"
said Petr. "Using the impactor block was a simple way to create a shock wave similar to an explosion."

A Mechanical Event Simulation analysis was performed with nonlinear material models to include
the effects of large deformation and large stress. Built-in result monitoring tools were used to track
the velocity of selected nodes, which enabled calculation of stress history curves. "ALGOR
Mechanical Event Simulation is a powerful and robust computer modeling tool for accurately
predicting shock wave energy transmission and reflection through different rock materials and
jointing interfaces as well as the complete stress-deformation characteristics of a non-homogeneous
rock mass," said Petr.

The inset photograph shows a microscopic view of the cemented grain structure
within a geomedium (rock mass). CSM's ALGOR finite element model simulated the grain lattice that is
typical of a hard rock mass. The yellow discs represent grain particles, which are cemented
together by the green bonding material. The purple impactor block strikes downward onto the top surface
of the green part, simulating the shock wave from a plastic explosive.

ALGOR analysis results showed with more precision than could be captured in experimental studies exactly
how shock wave velocity is affected by different material densities and different packing arrangements within
a geomedium. "ALGOR MES enables you to see inside the material at any time during the event to precisely
examine velocity, displacement, stress, strain and other results," said Petr. "It is a valuable tool for
studying a brief, dynamic event such as an explosion."

Knowing how differences in material density and patterns of particle grains can slow down a
shock wave will also aid in the development of shock-resistant materials. Currently, this
knowledge is being applied to the construction of explosives-resistant concrete.

A four-step sequence compares experimental and numerical results of shock wave propagation
at different times. Above, high-speed photographs of the photoelastic experimental results show
the order of fringes. Below, ALGOR MES results show maximum shear stresses along the Z axis.

Future Work

Petr's continuing research includes finite element modeling of additional
patterns of discs to further test the effect of the grain lattice on shock wave velocity.
Additionally, a colleague and coauthor of a recent paper, Keith J. Orgeron, P.E. of Integra
Engineering, Inc. in Houston, Texas has extended the study to three-dimensional modeling using
ALGOR software.

According to Petr, "This work has shown the importance of the interaction of strain waves with
discontinuities in fragmentation. We must know shock wave propagation characteristics in order
to be able to determine the effect of blast parameters on fragmentation."

Four frames illustrate a nonlinear dynamic FE analysis using an ALGOR model of a
lab test of shock wave propagation in a geomedium. Vertical, normal stress profiles indicate
the progression and reflections of the first pair of waves initiated in frame 1 and 2 as the
impactor (upper block) transfers its kinetic energy by compressing itself and
the second larger block (compression shown in gray and blue colors). Frame
3 shows the first development of a tensile stress intensity (tension shown
in yellow and red colors) capable of fracturing geomedia, and the complete
compression of the lower block. Frame 4 shows mixed standing wave patterns
as all blocks are independently propelled into space. [Scaling of
deformations = 100x, time steps < 0.000001 seconds.]
(Courtesy of Keith J. Orgeron, Integra Engineering, Inc.)

Vilem Petr, who is from the Czech Republic, comes from a long line of miners. His grandfather
was a coal miner and his father was an open-pit miner. In 1992, he graduated from the Technical
University in Mining in Ostrava, Czech Republic. He worked as a mining engineer for several years
before deciding to continue his education in the United States. He earned an M.S. in Mining
Engineering from New Mexico Institute of Mining and Technology and a Ph.D. in Mining and
Earth Systems Engineering from Colorado School of Mines.